Math 4513 (Senior Mathematics Seminar)

Fall 2005


John Albert
Office: PHSC 1004, Ext. 5-3782.
Office hours: Mon, Wed and Thurs, 2:30-3:30 PM (or by appointment)

  • Here is the take-home final exam. NOTE: As mentioned in class, there is an error on problem 2. The correct statement should be: "(i) among the points which are colored red, yellow, blue, and green, there do not exist any two points of the same color which are a distance of exactly TWO UNITS apart from each other. (ii) among the points which are colored purple and orange, there do not exist any two points of the same color which are exactly ONE UNIT apart from each other."
  • Here are solutions to the problems on the midterm exam. Problems 1 and 2 were worth 20 points each, problems 3(i) and 3(ii) were worth 15 points each, problem 4(i) was worth 10 points, and problem 4(ii) was worth 20 points. The little numbers in circles written on the solutions are rough indications of how I assigned partial credit.
  • Review sheet for the midterm exam.
  • Here is a handout on how the presentations will be graded, along with the current schedule for the presentations.
  • Syllabus for this course.
  • Here are the handouts Some unsolved problems in plane geometry and Some unsolved problems in number theory.


    Here is some material on the presentations.
  • Bauer/Rollins: Illuminating Polygons
  • Beebe/Stevens: Painting the Plane
  • Brawner/Zell: The Happy End Problem - A Tale of Romance
  • Cook/Schaefer: The Quest to Calculate Pi
  • Dizikes/T. Nguyen: The Perfect Cuboid Problem
  • Givens/Tran: Prime factorization - in polynomial time?
  • Harwell/Lewis: The Collatz problem
  • Harwood/Schwartz: Pushing Disks Together
  • Lerner/Pearce: Inscribed Squares in Closed Curves
  • Matulich/Pitts: Wasan and Sangaku - Japanese Temple Geometry
  • McCord/Perkins: Penrose Tiles
  • Miller/K. Nguyen: Relations between Pi and e
  • Monroe/C. Nguyen: The Four-Color Problem


  • Here are copies of Assignment 4, Assignment 3, Assignment 2, and Assignment 1.